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通过自动化回归进行 HAC 估计AI 解读

A simple regression approach to HAC and LRV estimation is suggested. The method exploits the fact that the quantities of interest relate to only one point of the spectrum (the origin). The new estimator is simply the explained sum of squares in a linear regression whose regressors are a set of trend basis functions. Positive definiteness in the estimate is therefore automatically enforced, and the technique can be implemented with standard regression packages. No kernel…

曲率度量与检验的非参数方法AI 解读

This article considers the problem of testing curvature (e.g., linearity, concavity, convexity) in a multivariate nonparametric regression model. A measure of curvature, called the simplex statistic, that does not require bandwidth choice and is easy to compute, is introduced. A global test of curvature based on the simplex statistic is also introduced. Localized versions of the test, which require smoothing parameters, are shown to be consistent against more general…

条件密度估计的交叉验证方法AI 解读

We extend the idea of crossvalidation to choose the smoothing parameters of the ‘double-kernel’ local linear regression for estimating a conditional density. Our selection rule optimises the estimated conditional density function by minimising the integrated squared error. We also discuss three other bandwidth selection rules, an ad hoc method used by Fan et al. (1996), a bootstrap method of Hall et al. (1999) for bandwidth selection in the estimation of conditional…

局部线性空间回归AI 解读

A local linear kernel estimator of the regression function x↦g(x):=E[Yi|Xi=x], x∈ℝd, of a stationary (d+1)-dimensional spatial process {(Y i,Xi),i∈ℤN} observed over a rectangular domain of the form ℐn:={i=(i1,…,iN)∈ℤN|1≤ik≤nk,k=1,…,N}, n=(n1,…,nN)∈ℤN, is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is…

从有限样本到渐近：样条回归选择准则的几何联系AI 解读

This paper studies, under the setting of spline regression, the connection between finite-sample properties of selection criteria and their asymptotic counterparts, focusing on bridging the gap between the two. We introduce a bias-variance decomposition of the prediction error, using which it is shown that in the asymptotics the bias term dominates the variability term, providing an explanation of the gap. A geometric exposition is provided for intuitive understanding. The…

平滑样条非线性非参数回归模型AI 解读

Almost all of the current nonparametric regression methods, such as smoothing splines, generalized additive models, and varyingcoefficients models, assume a linear relationship when nonparametric functions are regarded as parameters. In this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly. They arise in many fields as either theoretical or empirical models. Our new estimation methods…

空气污染与死亡率的改进半参数时间序列模型AI 解读

In 2002, methodological issues around time series analyses of air pollution and health attracted the attention of the scientific community, policy makers, the press, and the diverse stakeholders concerned with air pollution. As the U. S. Environmental Protection Agency (EPA) was finalizing its most recent review of epidemiologic evidence on particulate matter air pollution (PM), statisticians and epidemiologists found that the S–PLUS implementation of generalized additive…

非平稳面板时间序列长期平均关系的估计AI 解读

This paper proposes a new class of estimators of the long-run average relationship in nonstationary panel time series. The estimators are based on the long-run average variance estimate using bandwidth equal to T. The new estimators include the pooled least squares estimator and the fixed effects estimator as special cases. It is shown that the new estimators are consistent and asymptotically normal under both the sequential limit, wherein T → ∞ followed by n → ∞, and the…

解释变量存在测量误差时的非参数回归AI 解读

We introduce a nonparametric regression estimator that is consistent in the presence of measurement error in the explanatory variable when one repeated observation of the mismeasured regressor is available. The approach taken relies on a useful property of the Fourier transform, namely, its ability to convert complicated integral equations into simple algebraic equations. The proposed estimator is shown to be asymptotically normal, and its rate of convergence in probability…

利用间接测量对服务时间分布进行非参数推断AI 解读

Summary In studies of properties of queues, for example in relation to Internet traffic, a subject that is of particular interest is the ‘shape’ of service time distribution. For example, we might wish to know whether the service time density is unimodal, suggesting that service time distribution is possibly homogeneous, or whether it is multimodal, indicating that there are two or more distinct customer populations. However, even in relatively controlled experiments we may…

半参数密度估计中的信息合并AI 解读

Summary The density ratio model specifies that the likelihood ratio of m−1 probability density functions with respect to the mth is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt…

利用混合样条模型进行限制似然比失拟检验AI 解读

Summary Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one-sided testing problem a further complication is that the variance component…

条件矩限制模型中的经验似然推断AI 解读

This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our…

使用非高斯核的密度峰识别AI 解读

It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of the extent to which the number of modes is a nonmonotone function of bandwidth in the case of general compactly supported…

非参数函数的筛经验似然比检验AI 解读

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153–193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the case where the error distribution is completely unspecified via newly proposed…

贝叶斯一致性的新方法AI 解读

We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hellinger and Kullback–Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are also found and demonstrated on examples.

伪回归中具有极限分布的 t 统计量AI 解读

This paper investigates the asymptotic properties of the t-statistic in spurious regressions when the bandwidth in the estimation of the heteroskedasticity and autocorrelation consistent (HAC) standard error is set proportional to the sample size. Using autocovariances of large lags, the so-defined HAC estimator is capable of capturing the high persistence of the regressor and regression residuals. It is shown that the resulting t-statistic converges to a nondegenerate…

连续时间扩散模型中的自适应检验AI 解读

We propose an optimal test procedure for testing the marginal density functions of a class of nonlinear diffusion processes. The proposed test is not only an optimal one but also avoids undersmoothing. An adaptive test is constructed, and its asymptotic properties are investigated. To show the asymptotic properties, we establish some general results for moment inequalities and asymptotic distributions for strictly stationary processes under the α-mixing condition. These…

半变系数模型的有效估计AI 解读

Motivated by two practical problems, we propose a new procedure for estimating a semivarying‐coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h3 when a symmetric kernel is used, where h is the bandwidth, and the variance is of order n−1 and efficient in the semiparametric sense. Undersmoothing is unnecessary for the root‐n consistency of the estimators. Therefore, commonly used bandwidth selection…

受试者工作特征曲线的非参数置信区间AI 解读

We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug‐in rule for bandwidth choice,…

纵向数据半参数建模的新估计与模型选择程序AI 解读

Semiparametric regression models are very useful for longitudinal data analysis. The complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis. In this article, two new approaches are proposed for estimating the regression coefficients in a semiparametric model. The asymptotic normality of the resulting estimators is established. An…

通过似然基追踪进行变量选择与模型构建AI 解读

This article presents a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). In the setting of a tensor product reproducing kernel Hilbert space, we decompose the log-likelihood into the sum of different functional components such as main effects and interactions, with each component represented by appropriate basis functions. Basis functions are chosen to be compatible with variable selection and model…

广义加性模型中稳定高效的多重平滑参数估计AI 解读

Representation of generalized additive models (GAM's) using penalized regression splines allows GAM's to be employed in a straightforward manner using penalized regression methods. Not only is inference facilitated by this approach, but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross-validation. The current fitting and…

变系数模型中的平滑样条估计AI 解读

Summary Smoothing spline estimators are considered for inference in varying-coefficient models with one effect modifying covariate. Bayesian ‘confidence intervals’ are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators, fitted values, posterior variances and data-adaptive methods for selecting the levels of smoothing. The efficacy and utility of the methodology proposed are demonstrated through a small…